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Recent performance breakthroughs in Artificial intelligence (AI) and Machine learning (ML), especially advances in Deep learning (DL), the availability of powerful, easy-to-use ML libraries (e.g., scikit-learn, TensorFlow, PyTorch.), and…

Machine Learning · Computer Science 2023-03-24 Mahmoud Yaseen , Xu Wu

We analyze an ensemble-based approach for uncertainty quantification (UQ) in atomistic neural networks. This method generates an epistemic uncertainty signal without requiring changes to the underlying multi-headed regression neural network…

Chemical Physics · Physics 2025-11-21 Idan Fonea , Amir Peles , Sivan Niv , Goren Gordon , Amir Natan

Stochastic Gradient Descent (SGD) is a widely used tool in machine learning. In the context of Differential Privacy (DP), SGD has been well studied in the last years in which the focus is mainly on convergence rates and privacy guarantees.…

Machine Learning · Statistics 2024-05-22 Holger Dette , Carina Graw

Neural Network (NN) models provide potential to speed up the drug discovery process and reduce its failure rates. The success of NN models require uncertainty quantification (UQ) as drug discovery explores chemical space beyond the training…

Machine Learning · Computer Science 2022-11-01 Ya Ju Fan , Jonathan E. Allen , Kevin S. McLoughlin , Da Shi , Brian J. Bennion , Xiaohua Zhang , Felice C. Lightstone

The role of uncertainty quantification (UQ) in deep learning has become crucial with growing use of predictive models in high-risk applications. Though a large class of methods exists for measuring deep uncertainties, in practice, the…

Machine Learning · Statistics 2019-11-01 Bindya Venkatesh , Jayaraman J. Thiagarajan

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…

Machine Learning · Computer Science 2023-02-08 Apostolos F Psaros , Xuhui Meng , Zongren Zou , Ling Guo , George Em Karniadakis

Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large…

Machine Learning · Computer Science 2020-08-25 Lingkai Kong , Jimeng Sun , Chao Zhang

Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…

Machine Learning · Computer Science 2024-07-19 Frederik Hoppe , Claudio Mayrink Verdun , Hannah Laus , Felix Krahmer , Holger Rauhut

Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform…

Uncertainty Quantification (UQ) is crucial for ensuring the reliability of machine learning models deployed in real-world autonomous systems. However, existing approaches typically quantify task-level output prediction uncertainty without…

Computer Vision and Pattern Recognition · Computer Science 2025-03-27 Luke Chen , Junyao Wang , Trier Mortlock , Pramod Khargonekar , Mohammad Abdullah Al Faruque

Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable…

Machine Learning · Computer Science 2020-05-21 Lior Hirschfeld , Kyle Swanson , Kevin Yang , Regina Barzilay , Connor W. Coley

In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…

Numerical Analysis · Mathematics 2024-04-18 Lorenc Kapllani , Long Teng

State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible…

Computational Physics · Physics 2018-10-17 Rohit Tripathy , Ilias Bilionis

Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…

Machine Learning · Computer Science 2025-10-01 Alexander Fishkov , Kajetan Schweighofer , Mykyta Ielanskyi , Nikita Kotelevskii , Mohsen Guizani , Maxim Panov

Deep learning (DL) has shown great potential in medical image enhancement problems, such as super-resolution or image synthesis. However, to date, little consideration has been given to uncertainty quantification over the output image. Here…

A model's ability to express its own predictive uncertainty is an essential attribute for maintaining clinical user confidence as computational biomarkers are deployed into real-world medical settings. In the domain of cancer digital…

Large Language Models (LLMs) excel in text generation, reasoning, and decision-making, enabling their adoption in high-stakes domains such as healthcare, law, and transportation. However, their reliability is a major concern, as they often…

Computation and Language · Computer Science 2025-06-05 Xiaoou Liu , Tiejin Chen , Longchao Da , Chacha Chen , Zhen Lin , Hua Wei

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

Dynamical Systems · Mathematics 2007-05-23 Yu Zou , Ioannis G. Kevrekidis

Despite the popularity of Convolutional Neural Networks (CNN), the problem of uncertainty quantification (UQ) of CNN has been largely overlooked. Lack of efficient UQ tools severely limits the application of CNN in certain areas, such as…

Machine Learning · Computer Science 2026-04-15 Hongfei Du , Emre Barut , Fang Jin

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…

Probability · Mathematics 2020-06-08 Côme Huré , Huyên Pham , Xavier Warin